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What happened to five?

At 10:00 pm Saturday I returned home from #NCTMDenver. My daughters Gwyneth (8) and Keira (5) were glued to me for the next two and a half hours. Mostly playing with the Zometool kit I picked up at the exhibit hall, filling me in on the past five days.

“What should I click, Dad?” she asked. I was just about to reply “Doesn’t matter, just pick one” before I stopped myself. Instead, I told her to pick the best wrong answer. I was just curious, not trying to prepare my daughter for future success on bubble tests. “Six to eleven,” she quickly answered. Her confidence surprised me. “Nah, gotta be under 4,” I said.

With some prompting (needling?) she presented three arguments. First, Gwyneth reasoned that since Keira was “five and a bit” her sister was closer to six than four. She argued that it’s less than a year until her sixth birthday and it’s been over a year since her fourth birthday.

Second, she reasoned that “five and a bit” was more than five, the halfway point between four and six.

She gets it. Kids get it. They get that 37 is closer to 40 than 30. They get that 7.3 is less than halfway between 7 and 8. They get it until we ask them to memorize things like “Five and above? Give it a shove.”

Third, Gwyneth argued that since she is eight and her sister is five, the best answer is the one that includes the two of them. A stretch to connect this to measures of central tendency?

I’m not sure if Gwyneth enjoys finding these things for her dad or if she thinks it’s getting her one step closer to this: